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Green’s function representations for seismic interferometry Kees Wapenaar 75 th SEG meeting, Houston November 8, 2005

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Seismic interferometry : obtaining new seismic responses by X-correlation Claerbout, 1968 (1-D version) Schuster, 2001, 2004 (interferometric imaging) Weaver and Lobkis, 2001 (diffuse wave fields) Wapenaar, Draganov et al, 2002, 2004 (reciprocity) Derode et al., 2003 (time-reversal) Campillo and Paul, 2003 (surface waves) Snieder, 2004 (stationary phase) Bakulin and Calvert, 2004 (virtual source) Gerstoft, Sabra et al., 2004 (surface wave tomography) Van Manen, Robertsson & Curtis 2005 (modeling)

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Rayleigh’s reciprocity theorem:

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State A

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Rayleigh’s reciprocity theorem: State A State B

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Rayleigh’s reciprocity theorem: Time-reversal:

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Rayleigh’s reciprocity theorem: Time-reversal:

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Rayleigh’s reciprocity theorem: State A

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Rayleigh’s reciprocity theorem: State B

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Monopole at x

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Dipole at x

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High-frequency approximation

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High-frequency approximation Far-field approximation (Fraunhofer)

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High-frequency approximation Far-field approximation (Fraunhofer)

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Rayleigh’s reciprocity theorem:

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Free surface

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High-frequency approximation

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Free surface High-frequency approximation Far-field approximation (Fraunhofer)

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Free surface High-frequency approximation Far-field approximation (Fraunhofer)

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Free surface

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Uncorrelated noise sources

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Draganov and Wapenaar, Poster session PSC P1, Today

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Draganov et al., EAGE, 2003

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Draganov and Wapenaar, Poster session PSC P1, Today

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From acoustic …………….. …. to elastodynamic ………

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Draganov and Wapenaar, Poster session PSC P1, Today

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Conclusions Exact and approximate representations of Green’s functions for seismic interferometry Main contributions come from stationary points Free surface obviates the need of closed integral along sources Uncorrelated noise sources obviates the need of integral along sources Random source distribution suppresses artefacts from scatterers below sources Straightforward extension to elastodynamic situation

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